Page curves for general interacting systems
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We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work , where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, (S2(ℓ) = − ln K(β) + ℓ ln a(β) − ln 1+a(β)−L+2ℓ), where L is the total volume of the system and a and K are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.
KeywordsLattice Quantum Field Theory Random Systems Conformal Field Theory
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- P. Calabrese and J. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002.Google Scholar
- P. Calabrese and J. Cardy, Quantum quenches in extended systems, J. Stat. Mech. (2007) P06008.Google Scholar
- M. Hotta and A. Sugita, The fall of the black hole firewall: natural nonmaximal entanglement for the page curve, Prog. Theor. Exp. Phys. 2015 (2015) 123B04.Google Scholar
- M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994) 888.Google Scholar
- Y. Huang, Universal eigenstate entanglement of chaotic local hamiltonians, to be published Nucl. Phys. (2018).Google Scholar
- I. Dumitriu, Eigenvalue statistics for beta-ensembles, technical report (2003).Google Scholar
- S.A. Blanco and T.K. Petersen, Counting Dyck paths by area and rank, arXiv:1206.0803.
- T. Mansour and Y. Sun, Identities involving Narayana polynomials and Catalan numbers, arXiv:0805.1274.
- N.M. Temme, Asymptotic methods for integrals, Series in Analysis volume 6, World Scientific, Hackensack U.S.A. (2015).Google Scholar